I finally videotaped myself doing the lifts. The biggest thing to stand out was when I receive the bar in the C&J my elbows are down. What's the best way to correct this while doing the CA WOD? What drills should I focus on in my warm-up?

Make sure you're releasing your grip on the bar soon enough and completely enough - once the forearms are about vertical, those hands can open up. Gripping tight past this point will slow the elbows down. Other than that, you can try muscle cleans, tall cleans, and isolate the rack delivery from a scarecrow position.